Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 652 · 40 sums

The method (Letters one side, numbers the other): Open brackets: a(x − b) = ax − ab. Fractions: multiply both sides by the LCM of the denominators — x/3 + x/4 = 14 → 4x + 3x = 168. Move letter terms to one side and numbers to the other (change the sign when a term crosses =), then divide. Word problems: consecutive numbers are n, n + 1, n + 2 …; ages in y years are age + y.

1. 1.Solve: 4(m − 2) = 2m + 6. What is m?
2. 2.A father is 7 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
3. 3.Solve: 8n + 15 = 7n + 29. What is n?
4. 4.A father is 18 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
5. 5.Solve: m/4 + m/3 = 56. What is m?
6. 6.Solve: 3n + 19 = n + 43. What is n?
7. 7.The sum of four consecutive whole numbers is 210. What is the smallest of them?
8. 8.Solve: 4y + 12 = 2y + 36. What is y?
9. 9.The length of a rectangle is 1 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
10. 10.Solve: 4y + 12 = 3y + 26. What is y?
11. 11.Solve: 5(x − 2) = 3x + 18. What is x?
12. 12.The length of a rectangle is 12 cm more than its width. Its perimeter is 48 cm. What is its width (in cm)?
13. 13.Solve: x/2 + x/4 = 15. What is x?
14. 14.A father is 36 years older than his son. In 7 years, the father will be three times as old as his son. How old is the son now?
15. 15.Solve: p/3 + p/6 = 18. What is p?
16. 16.The length of a rectangle is 15 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
17. 17.The sum of two consecutive whole numbers is 45. What is the smallest of them?
18. 18.The sum of two consecutive whole numbers is 117. What is the smallest of them?
19. 19.A father is 20 years older than his son. In 6 years, the father will be three times as old as his son. How old is the son now?
20. 20.Solve: m/5 + m/3 = 8. What is m?
21. 21.Solve: 6(x − 4) = x + 6. What is x?
22. 22.Solve: 6y + 11 = 4y + 21. What is y?
23. 23.Solve: 5y + 2 = 3y + 4. What is y?
24. 24.A father is 10 years older than his son. In 3 years, the father will be three times as old as his son. How old is the son now?
25. 25.Solve: 7n + 16 = n + 28. What is n?
26. 26.The sum of four consecutive whole numbers is 206. What is the smallest of them?
27. 27.A father is 10 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
28. 28.Solve: t/6 + t/4 = 35. What is t?
29. 29.The length of a rectangle is 1 cm more than its width. Its perimeter is 14 cm. What is its width (in cm)?
30. 30.A father is 30 years older than his son. In 7 years, the father will be four times as old as his son. How old is the son now?
31. 31.A father is 48 years older than his son. In 7 years, the father will be four times as old as his son. How old is the son now?
32. 32.The length of a rectangle is 13 cm more than its width. Its perimeter is 106 cm. What is its width (in cm)?
33. 33.A father is 8 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
34. 34.The length of a rectangle is 10 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
35. 35.The sum of four consecutive whole numbers is 114. What is the largest of them?
36. 36.Solve: 6(t − 2) = 3t + 12. What is t?
37. 37.Solve: 3m + 6 = m + 8. What is m?
38. 38.The sum of four consecutive whole numbers is 138. What is the largest of them?
39. 39.Solve: x/3 + x/2 = 15. What is x?
40. 40.The length of a rectangle is 14 cm more than its width. Its perimeter is 100 cm. What is its width (in cm)?

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